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Henrici P. — Applied and Computational Complex Analysis (Vol. 3)
Henrici P. — Applied and Computational Complex Analysis (Vol. 3)



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Название: Applied and Computational Complex Analysis (Vol. 3)

Автор: Henrici P.

Аннотация:

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.


Язык: en

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 637

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Mean value property      220 222 232 241
Measure, harmonic      248 250 251 252 255 440 441 448 453
Mehrstellenverfahren      303 305 309 317 320 321 322
Melentiev’s method      412
Mergelyan’s theorem      558 571
Milin conjecture      584 591 599 600
Minimum phase network      211
Model, of error propagation      12 14 16
Modulation, single side-band      205 207 209
Modulation, single side-band, inversion of      209
Modulus of doubly connected region      450 456 477 503
Modulus of quadrilateral      430 431 432 434 435 436 437 439 440
Modulus, logarithmic      450 456
Moebius transformation      193 230 244 249 331 365 368 369 429 430 574
Monotonicity      241 242
Multiplication of formal power series      72
Multiplication of large integers      65 71
Multiplication of polynomials      64
Neumann function      269 271 272 394 490 494 547
Neumann kernel      280 282 284
Neumann kernel, parametric      394 395 397
Neumann problem      263 264 265 266 267 268 269 270 286 490 494
Neumann problem, generalized      264
Nevanlinna representation formula      366
Newton — Cotes formula      17
Newton’s method      72 73 74 75 77 80 427 428
Newton’s method in function space      413
Norm      306 531
Norm of element in $\Pi_n$      3 81
Norm, Euclidean      10
Operator, adjoint      5
Operator, isometric      5
Operator, linear      3
Operator, unitary      44
Orthogonalization      507 535 553
Osculation algorithm      328 335 341 342 344 370 406
Osculation algorithm, speed of convergence of      338
Osculation family      329 331 333 340 343 344 457 461
Osgood — Caratheodory theorem      126 259 346 351 355 360 379
Parameter problem for Schwarz — Christoffel map      423
Parameter problem, generalized      428
Parseval’s relation      538
Period      219
Period cube      81
Period vector      80 81
Period, conjugate      219 220 453
Perturbation method, for Theodorsen’s equation      412
Phase characteristic      211
Pixel      85
Plate, clamped      313
Plemelj formula      see “Sokhotskyi formula
Poincare — Bertrand formula      118
Point, active      303
Point, interior, of arc      89
Point, regular      303
Poisson kernel      225 226 228 248
Poisson sum formula      28 29 30
Poisson’s equation      214 294 295 299 300 301 302 307 311 312 313 314
Poisson’s formula      112 225 226 228 229 230 231 232 246 249 267 287 356
Pole, of fundamental singularity      255 258
Polynomial, length of      72
Polynomial, multiplication of      64 65
Polynomial, orthogonal      137 139 140 142 143 151
Polynomial, orthogonal, in region      543
Polynomial, orthogonal, on curve      555
Polynomial, self-reciprocal      130 418
Polynomial, trigonometric      43 401
Polynomial, trigonometric interpolating      44 45 47
Polynomial, trigonometric interpolating, conjugate of      49 50
Polynomial, trigonometric interpolating, error of      45
Polynomial, zeros of      36 67
Pompeiu’s formula      289 290 291 301
Potential of double layer      276 277 280 285
Potential of single layer      273 279 281 377 382 384
Potential, logarithmic      273 274 295 297 299 301
Power series, formal      71
Power spectrum      59 60
Power spectrum, smoothed      61
Power sum      37
Precision constant      11
Prevertex      423 478 481 482
Principal value integral      89 90 91 102 141 148 200 394
Principal value integral, inversion of      116
Principal value integral, series expansion of      139
Privalov problem      119 127 128 134 151 417
Privalov problem for arc      163 164 167 168 171 178 184
Privalov problem for closed curve      120 123 125 126
Privalov problem, homogeneous      119 120 131
Privalov problem, solution of      119 163
Product theorem      212
Product, infinite      260
Quadrilateral      428 429 432 434 441 443
Quadrilateral, conformally equivalent      429 431
Quadrilateral, L-shaped      438 441
Quadrilateral, reciprocal      432
Quadrilateral, symmetric      433 439
Quotient-difference algorithm      138 322
Radius, inner      388 389
Radius, outer      389
rectangle      312 313 376 431 487
Region, circular      488 496
Region, non-degenerate doubly connected      445
Region, totally resectable      501
Regularization      393
Relaxation factor      406
Representation of analytic function      132
Representation of set      131
Reproducing property      271 548 553
Residue      106 291 546
Residue of formal Laurent series      508
Reversion of formal Laurent series      510 513
Reversion of formal power series      72
Reversion operator      3 62
Richardson extrapolation      38
Riemann family      334 460
Riemann mapping function      371 373 547 551 554 558
Riemann mapping theorem      324 328 329 338 451
Riemann problem      108 126 128 129 130 131 132 133 134 135 136 413 417 418 419 422
Riemann’s theorem      236
Robertson’s conjecture      581
Romberg algorithm      20 21 545
Rotation, total, of boundary curve      525
Rouche’s Theorem      588 589 597
Rounding error of convolution      63
Rounding error of fast Fourier transform      13 66
Saalschutz formula      607
Sampling point      17
Sampling theorem      30
Sampling value      17
Schmiegungsverfahren      see “Osculation algorithm”
Schur — Jabotinsky theorem      512
Schwaiz — Christoffel formula      423 478 480 521
Schwarz formula      102 103 112 225 528 595
Schwarz formula for upper half-plane      196 197
Schwarz lemma      253 254 325 331 335 336 337 368 593
Schwarz reflection principle      232 363 596
Schwarz — Christoffel map      323 376 422 424 427 444 483 579 580
Separation ratio      67 68 71
Shift operator      3 4 62
Side, of curve      92
signal      27 205 206 207
Signal, analytic      209 210
Signal, band-limited      29 30
Signal, Gaussian      30
Signal, modulated      208
Signal, time-limited      29 30
Signum function      41
Single-slit map      587 590 591 593
Singularity, essential, of harmonic function      237
Singularity, isolated, of harmonic function      235 243
Singularity, logarithmic      163 166 168
Singularity, removable, of harmonic function      236
Singularity, weak      162 166 171 172 176 177 189
Skew derivative problem      136
Slit map      333
Smoothing      55 62
Smoothing sequence      55
Sokhotskyi, formula of      94 95 99 100 102 105 107 109 113 115 117 118 120 124 132 138 140 153 161 164 170 171 179 181 194 196 278 279 280 281 387 394 395 396 397 465 466 467 562 563
Solution, canonical for arc      165 167 168 169 170 171
Solution, canonical, in sense of divergence theorem      295 297
Solution, canonical, of Privalov problem      130 131
Solution, canonical, recessive, of difference equation      141
Space, linear      491 530
Space, normed      3 531
Spectrum      27 199 200 201 205 207
Spectrum, approximate      28
Stability, mathematical      9
Stability, numerical      9 10
Standard parametrization      593
Steklov eigenvalue      494 496
Stencil      304 305 309 313
Stieltjes transform      137
Stieltjes — Perron inversion formula      137 138
Stirling’s formula      38
Symmetry property of Green’s function      258
Symmetry property of Neumann’s function      271
Symmetry, with respect to curve      499
System, orthonormal      534 535 539 540 545
System, orthonormal, complete      537 540 542 552
Szego kernel function      553 555 564 569
Taylor expansion      115 124 322 541 571
Taylor’s formula, for formal power series      73
Theodorsen, method of      403 407 413 470
Time series      59
Time window      61
Timman’s method      409 413 477 478
Translation theorem      208
Transplantation, conformal      222 246 252 259 267 432 434 442
Triangularization      308 435
Trilateral      428 429 443
Twist      16
Underrelaxation      406
Unit sequence      3
Vandermonde’s formula      604
Variational method      303 305
Variations, calculus of      491
Vekua’s representation theorem      136
Vitali’s theorem      589
Volterra equation      78
Warschawski — Lichtenstein theorem      359 380
Wegmann’s method      416 417 419 422 478 506
Wegmann’s method for exterior map      422
Winding number      447 452 462 463 483 520
Wirtinger derivative      287 294 298 300 551
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